1st Grade Mathematics

PS 172 is dedicated to a project-based, problem-solving, approach to mathematics that allows student to engage in hands-on, relatable experiences. Our mathematics program is based on the Engage NY curriculum and incorporates projects throughout the year. We are committed to having students take ownership of their learning and construct meaning in math, choosing which strategies work best, for them to solve complex word problems. Students are encouraged to explore different strategies and explain and justify their reasoning when solving. Common models, teaching strategies, and problem solving strategies are used to help students progress through each grade level.

Sequence of ModulesModule 1: Sums and Differences to 10Module 2: Introduction to Place Value Through Addition and Subtraction Within 20Module 3: Ordering and Comparing Length Measurements as NumbersModule 4: Place Value, Comparison, Addition and Subtraction to 40Module 5: Identifying, Composing, and Partitioning ShapesModule 6: Place Value, Comparison, Addition and Subtraction to 100

Module 1: Sums and Differences to 10In this first module of Grade 1, students make significant progress towards fluency with addition and subtraction of numbers to 10 as they are presented with opportunities intended to advance them from counting all to counting on, which leads many students then to decomposing and composing addends and total amounts. In Kindergarten, students achieved fluency with addition and subtraction facts to 5. This means they can decompose 5 into 4 and 1, 3 and 2, and 5 and 0. They can do this without counting all. They perceive the 3 and 2 embedded within the 5.

Module 2: Introduction to Place Value through Addition and Subtraction to 20

Module 2 serves as a bridge from problem solving within 10 to work within 100 as students begin to solve addition and subtraction problems involving teen numbers. In Module 1, students were encouraged to move beyond the Level 1 strategy of counting all to the more efficient counting on. Now, they go beyond Level 2 to learn Level 3 decomposition and composition strategies, informally called make ten or take from ten.We will launch this module through out Inventory Project. Help!! Other classes are borrowing our supplies and we need a system to keep track of what we have, what people are borrowing, and what they are returning. Students will develop strategies to count classroom supplies such as counting cubes, scissors, and markers to keep track of how many of each item they have. They will develop the bundling/grouping strategy to make tens to help them count more efficiently and use this context to develop addition and subtraction strategies. Children can apply these strategies at home when organizing their toys or household items.

Module 3: Ordering and Comparing Length Measurements as Numbers

In this 13-day module, students will use non-standard units to measure objects, and will compare and order objects by length. Module 3 opens by extending students’ Kindergarten experiences with direct length comparison to the new learning of indirect comparison whereby the length of one object is used to compare the lengths of two other objects. “My string is longer than your book. Your book is longer than my pencil. That means my string is longer than my pencil!” Students use the same transitivity, or indirect comparison, to compare short distances within the classroom in order to find the shortest path to their classroom door, which is helpful to know for lining up and for emergencies. This module takes longer than and shorter than to a new level of precision by introducing the idea of a length unit. Centimeter cubes are laid alongside the length of an object as students learn that the total number of cubes laid end to end with no gaps or overlaps represents the length of that object. Students will then explore the usefulness of measuring with similar units. Students measure the same objects from Topic B using two different non-standard units, toothpicks and small paper clips, simultaneously to measure one object and answer the question, “Why do we measure with same-sized length units?” They realize that using iterations of the same unit will yield consistent measurement results. Similarly, students explore what it means to use a different unit of measurement from their classmates. It becomes obvious to students that if we want to have discussions about the lengths of objects, we must measure with the same units. This module closes as students represent and interpret data. They collect data about their classmates and sort that information into three categories. Using same-sized pictures on squares, students represent this sorted data so that it can be easily compared and described.

Module 4: Place Value, Comparison, Addition and Subtraction to 40 and the​The Design a Game ProjectIn this 35-day module, students will study, organize, and manipulate numbers within 40. They will compare number quantities, using the symbols for greater and less than (>, <). Students will work with adding and subtracting tens and will begin to add two-digit numbers. The place value chart at this point in 1st grade consists of two boxes; the one on the left labeled “tens” and the one on the right labeled “ones”. Students will be asked initially to match a number of objects with the correct representation on the place value chart. Later, they use the chart more abstractly to add two-digit numbers. Incorporated throughout this module is “The Design a Game Project” where students will work in small groups to create their own game (card game, board game, memory game) that will help them practice the skills and strategies they are learning throughout the module to add and subtract.

Module 5: Identifying, Composing, and Partitioning Shapes and the Build A City Project

In Module 5, students consider part–whole relationships through a geometric lens. The module opens with students identifying the defining parts, or attributes, of two- and three-dimensional shapes, building on their kindergarten experiences of sorting, analyzing, comparing, and creating various two- and three-dimensional shapes and objects. Students combine shapes to create a new whole: a composite shape. They also relate geometric figures to equal parts and name the parts as halves and fourths. The module closes with students applying their understanding of halves to tell time to the hour and half hour.

Module 6: Place Value, Comparison, Addition and Subtraction to 100

In this final module of the Grade 1 curriculum, students bring together their learning from Module 1 through Module 5 to learn the most challenging Grade 1 standards and celebrate their progress. As the module opens, students grapple with comparative word problem types. Next, they extend their understanding of and skill with tens and ones to numbers to 100. Students also extend their learning from Module 4 to the numbers to 100 to add and subtract. At the start of the second half of Module 6, students are introduced to nickels and quarters, having already used pennies and dimes in the context of their work with numbers to 40 in Module 4. Students use their knowledge of tens and ones to explore decompositions of the values of coins. The module concludes with fun fluency festivities to celebrate a year's worth of learning.

How you can help at home:

Practice “counting on” as a strategy for addition, e.g. if you have 7 LEGO pieces, and then you get 3 more, encourage your student to start with the number 7 and count “8…9…10” to find the total.

Discuss various ways to take apart a given number, e.g. 6 is made of 1 and 5, 2 and 4, 3 and 3, etc.

Talk about how we can find “tens” in other, large numbers

Make up and discuss short story problems that involve simple addition and subtraction

Give your student as many opportunities to measure objects using other, smaller objects, e.g. “How many Lego pieces long is your book? How many blueberries long is this notebook?

Continue to practice adding and subtracting within 20.

Continue to ask your student to compare two different quantities, using the language “greater than” and “less than”.